Page 339 - Advanced thermodynamics for engineers

328 CHAPTER 15 COMBUSTION AND FLAMES

Table 15.1 Flammability and Explosion Limits (Mixtures Defined in % Volume) (at Ambient
Temperature and Pressure) (Lewis and von Elbe (1961), data also in wiki (2014))
Lean Rich
Mixture Flammability Explosion Flammability Explosion Stoichiometric
H 2 eair 4 18 74 59 29.8
COeO 2 16 38 94 90 66.7
COeair 12.5 74 29.8
NH 3 eO 2 15 25 79 75 36.4
C 3 H 8 eO 2 2 3 55 37 16.6
CH 4 eair 5.3 15 9.51
C 2 H 6 eair 3.0 12.5 5.66
C 3 H 8 eair 2.2 9.5 4.03
C 4 H 10 eair 1.9 8.5 3.13

The steady state condition for the formation of radicals is

d½RŠ
¼ 0 ¼ k 1 ½MŠþ k 2 ða 1Þ½RŠ½MŠ k 3 ½RŠ½MŠ k 4 ½RŠ k 5 ½RŠ: (15.4)
dt
Solving Eqn (15.4) for R and substituting into Eqn (15.3) gives
2
d½PŠ k 1 k 2 ½MŠ
¼ : (15.5)
dt fk 3 ½MŠþ k 4 þ k 5 k 2 ða 1Þ½MŠg
The rate of production of the product P becomes infinite when the denominator is zero, giving

k 3 ½MŠþ k 4 þ k 5 k 3 k 4 þ k 5
a crit ¼ 1 þ ¼ 1 þ þ : (15.6)
k 2 ½MŠ k 2 k 2 ½MŠ
Thus, if a react > a crit the reaction is explosive: if the a react < a crit then the combustion is
nonexplosive and progresses at a finite rate. A few explosion limits, together with flammability limits
are listed in Table 15.1. This text will concentrate on nonexplosive mixtures from now on.

15.4 FLAMES
A flame is the usual mechanism by which combustion of hydrocarbons takes place in air. It is the
region where the initial breakdown of the fuel molecules occurs. There are two different types of flame,
as described above: premixed flames and diffusion flames. Premixed flames will be dealt with first
because it is easier to understand their mechanism.

15.4.1 PREMIXED FLAMES
Premixed flames occur in any homogeneous mixture where the fuel and the oxidant are mixed prior to
the reaction. Examples are the Bunsen burner flame and the flame in most spark-ignited engines.
Premixed flames can progress either as deflagration or detonation processes. This text will consider